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Hopf bifurcation of a multiple-delayed predator–prey system with habitat complexity

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  • Wang, Shufan
  • Tang, Haopeng
  • Ma, Zhihui

Abstract

This paper proposes a multiple-delayed predator–prey system with habitat complexity and harvesting effort, and investigates the dynamical behavior including stability properties and Hopf bifurcation. Firstly, stability of equilibrium points and the existence of Hopf bifurcation are investigated and some critical conditions which guarantee the corresponding results are obtained based on mathematical view. Secondly, the explicit formulae for determining the direction, stability and period of the bifurcating periodic solutions are derived by using the center manifold theory and the normal form theory. Finally, in order to verify the theoretical results, some numerical simulations are done to illustrate the results. It is observed that the level of abundance of prey and predator populations depends on the gestation delay if the gestation delay exceeds some critical values.

Suggested Citation

  • Wang, Shufan & Tang, Haopeng & Ma, Zhihui, 2021. "Hopf bifurcation of a multiple-delayed predator–prey system with habitat complexity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 1-23.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:1-23
    DOI: 10.1016/j.matcom.2020.08.008
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    References listed on IDEAS

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    1. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
    2. Moghadas, S.M. & Corbett, B.D., 2008. "Limit cycles in a generalized Gause-type predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1343-1355.
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    Cited by:

    1. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    2. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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